Tracking Eigenvalues to the Frontier of Moduli Space I: Convergence and Spectral Accumulation
نویسنده
چکیده
Let M and N be a compact differentiable manifolds of dimension d and d + 1 respectively. Given a compact interval I ⊂ R, we suppose that we have a (fixed) embedding I ×M ⊂ N . See figure 1. Let N denote the complement of {0} ×M . Let h be a Riemannian metric on M , and let ρ be a positive function on R that is positively homogeneous of degree 1 and smooth away from (0, 0). Given (a, b) ∈ R, we consider continuous families, gǫ, of symmetric (0, 2)-tensors on N such that
منابع مشابه
Tracking Eigenvalues to the Frontier of Moduli Space Ii: Limits for Eigenvalue Branches
Let I ⊂ R be a compact interval symmetric about 0. Let M and N , be compact oriented smooth manifolds of dimensions d and d+1 respectively. We suppose that we have an embedded copy of I ×M inside of N . (See Figure 1). Let N denote the complement of the hypersurface {0} ×M . We consider families ǫ → g(ǫ) of Riemannian metric (tensors) on N each of whose restriction to I ×M is a warped product o...
متن کاملThe spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions
Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...
متن کاملSIGNLESS LAPLACIAN SPECTRAL MOMENTS OF GRAPHS AND ORDERING SOME GRAPHS WITH RESPECT TO THEM
Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$ and $A(G)$ the adjacency matrix of $G$. The signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...
متن کاملSharp Bounds on the PI Spectral Radius
In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.
متن کاملPareto-optimal Solutions for Multi-objective Optimal Control Problems using Hybrid IWO/PSO Algorithm
Heuristic optimization provides a robust and efficient approach for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. The convergence rate and suitable diversity of solutions are of great importance for multi-objective evolutionary algorithms. The focu...
متن کامل